Univalent σ-harmonic mappings: applications to composites

Giovanni Alessandrini; Vincenzo Nesi

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 7, page 379-406
  • ISSN: 1292-8119

Abstract

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This paper is part of a larger project initiated with [2]. The final aim of the present paper is to give bounds for the homogenized (or effective) conductivity in two dimensional linear conductivity. The main focus is therefore the periodic setting. We prove new variational principles that are shown to be of interest in finding bounds on the homogenized conductivity. Our results unify previous approaches by the second author and make transparent the central role of quasiconformal mappings in all the two dimensional G-closure problems in conductivity.

How to cite

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Alessandrini, Giovanni, and Nesi, Vincenzo. "Univalent σ-harmonic mappings: applications to composites." ESAIM: Control, Optimisation and Calculus of Variations 7 (2010): 379-406. <http://eudml.org/doc/90627>.

@article{Alessandrini2010,
abstract = { This paper is part of a larger project initiated with [2]. The final aim of the present paper is to give bounds for the homogenized (or effective) conductivity in two dimensional linear conductivity. The main focus is therefore the periodic setting. We prove new variational principles that are shown to be of interest in finding bounds on the homogenized conductivity. Our results unify previous approaches by the second author and make transparent the central role of quasiconformal mappings in all the two dimensional G-closure problems in conductivity. },
author = {Alessandrini, Giovanni, Nesi, Vincenzo},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Effective properties; harmonic mappings; composite materials; quasiregular mappings.; effective properties; quasiregular mappings; two-dimensional linear conductivity},
language = {eng},
month = {3},
pages = {379-406},
publisher = {EDP Sciences},
title = {Univalent σ-harmonic mappings: applications to composites},
url = {http://eudml.org/doc/90627},
volume = {7},
year = {2010},
}

TY - JOUR
AU - Alessandrini, Giovanni
AU - Nesi, Vincenzo
TI - Univalent σ-harmonic mappings: applications to composites
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 7
SP - 379
EP - 406
AB - This paper is part of a larger project initiated with [2]. The final aim of the present paper is to give bounds for the homogenized (or effective) conductivity in two dimensional linear conductivity. The main focus is therefore the periodic setting. We prove new variational principles that are shown to be of interest in finding bounds on the homogenized conductivity. Our results unify previous approaches by the second author and make transparent the central role of quasiconformal mappings in all the two dimensional G-closure problems in conductivity.
LA - eng
KW - Effective properties; harmonic mappings; composite materials; quasiregular mappings.; effective properties; quasiregular mappings; two-dimensional linear conductivity
UR - http://eudml.org/doc/90627
ER -

References

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